An empirical Bayes approach for estimating skill models for professional darts players
File(s)
Accepted version
Author(s)
Haugh, Martin
Wang, Chun
Type
Journal Article
Abstract
We perform an exploratory data analysis on a data-set for the top 16 professional darts
players from the 2019 season. We use this data-set to fit player skill models which can
then be used in dynamic zero-sum games (ZSGs) that model real-world matches between
players. We propose an empirical Bayesian approach based on the Dirichlet-Multinomial
(DM) model that overcomes limitations in the data. Specifically we introduce two DM based skill models where the first model borrows strength from other darts players and the
second model borrows strength from other regions of the dartboard. We find these DM-based
models outperform simpler benchmark models with respect to Brier and Spherical scores,
both of which are proper scoring rules. We also show in ZSGs settings that the difference
between DM-based skill models and the simpler benchmark models is practically significant.
Finally, we use our DM-based model to analyze specific situations that arose in real-world
darts matches during the 2019 season.
players from the 2019 season. We use this data-set to fit player skill models which can
then be used in dynamic zero-sum games (ZSGs) that model real-world matches between
players. We propose an empirical Bayesian approach based on the Dirichlet-Multinomial
(DM) model that overcomes limitations in the data. Specifically we introduce two DM based skill models where the first model borrows strength from other darts players and the
second model borrows strength from other regions of the dartboard. We find these DM-based
models outperform simpler benchmark models with respect to Brier and Spherical scores,
both of which are proper scoring rules. We also show in ZSGs settings that the difference
between DM-based skill models and the simpler benchmark models is practically significant.
Finally, we use our DM-based model to analyze specific situations that arose in real-world
darts matches during the 2019 season.
Date Issued
2024-12-17
Date Acceptance
2024-06-11
Citation
Journal of Quantitative Analysis in Sports, 2024, 20 (4), pp.385-404
ISSN
1559-0410
Publisher
De Gruyter
Start Page
385
End Page
404
Journal / Book Title
Journal of Quantitative Analysis in Sports
Volume
20
Issue
4
Copyright Statement
Copyright © 2024 Walter de Gruyter GmbH, Berlin/Boston. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Identifier
https://www.degruyter.com/document/doi/10.1515/jqas-2023-0084/html
Publication Status
Published
Date Publish Online
2024-07-15